Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field

In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in H2(R3) are obtained by introducing a new linearized system with respect to (nγ−n˜γ,n−n˜,P−P˜,u,H) for constants n˜≥0 and P˜>0, and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of (n−n˜,nγ−n˜γ) in H2(R3) norm.